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Simplifying 7x(3x + -7) = 43 Reorder the terms: 7x(-7 + 3x) = 43 (-7 * 7x + 3x * 7x) = 43 (-49x + 21x2) = 43 Solving -49x + 21x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + -49x + 21x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -49x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -2.047619048 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '2.047619048' to each side of the equation. -2.047619048 + -2.333333333x + 2.047619048 + x2 = 0 + 2.047619048 Reorder the terms: -2.047619048 + 2.047619048 + -2.333333333x + x2 = 0 + 2.047619048 Combine like terms: -2.047619048 + 2.047619048 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + 2.047619048 -2.333333333x + x2 = 0 + 2.047619048 Combine like terms: 0 + 2.047619048 = 2.047619048 -2.333333333x + x2 = 2.047619048 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 2.047619048 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 2.047619048 + 1.361111112 Combine like terms: 2.047619048 + 1.361111112 = 3.40873016 1.361111112 + -2.333333333x + x2 = 3.40873016 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 3.40873016 Calculate the square root of the right side: 1.846274671 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.846274671 and -1.846274671.Subproblem 1
x + -1.166666667 = 1.846274671 Simplifying x + -1.166666667 = 1.846274671 Reorder the terms: -1.166666667 + x = 1.846274671 Solving -1.166666667 + x = 1.846274671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.846274671 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.846274671 + 1.166666667 x = 1.846274671 + 1.166666667 Combine like terms: 1.846274671 + 1.166666667 = 3.012941338 x = 3.012941338 Simplifying x = 3.012941338Subproblem 2
x + -1.166666667 = -1.846274671 Simplifying x + -1.166666667 = -1.846274671 Reorder the terms: -1.166666667 + x = -1.846274671 Solving -1.166666667 + x = -1.846274671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.846274671 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.846274671 + 1.166666667 x = -1.846274671 + 1.166666667 Combine like terms: -1.846274671 + 1.166666667 = -0.679608004 x = -0.679608004 Simplifying x = -0.679608004Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.012941338, -0.679608004}
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